Say you have an object that is sufficiently important, even if only for its sentimental value, that simply throwing it away when it wears out isn't an option. Instead, it gets replaced in piecemeal fashion: old and rotting timbers get replaced, rips and tears get patched, missing limbs and organs get prosthetics. As this process repeats, the thing in question is made up less and less of its original parts and more and more of replacements to the point that, one day, you simply aren't going to have anything of the original left. The question is, once this happens, is it still the original object or not?

More properly known as the "Ship of Theseus" or "Grandfather's Axe" paradox, this trope presents a classic philosophical conundrum. While it's often played for comedy, as common wisdom would suggest that, no, it's not still the same axe once its head and handle have both been replaced (though its owner will stubbornly insist to the contrary), sometimes it has more dramatic implications: if a person has his brain gradually replaced with electronics, for example, at what point do we cease to have a human with bits of machine in their brain and start to have a machine with bits of human in its brain? Do we ever? This scenario can also get thorny if someone rebuilds the thing in question from the discarded parts: if you have both a "new" thing made from the original material and an "original" thing made from new material, which one, if either, is the "real" one?

Examples

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Anime and Manga

This gets addressed in One Piece when the Straw Hats are hoping to repair their ship, the Going Merry. Because the keel (essentially the backbone of any ship) is severely cracked though, the ship is declared irreparable. When Luffy suggests they just build a "new Going Merry", it's pointed out that even if the shipwrights built a new ship precisely like the present Going Merry, it wouldn't be the same ship and the crew would definitely feel that it wasn't the same ship, even if it was built the exact same way.

Although said shipwrights do explain that, even if a new ship was built to the Merry's specifications, it actually wouldn't end up being precisely the same, because of inevitable variations in the construction material. This is the main reason given for why a replacement Merry would feel 'different', making this more of a practical concern than a philosophical one.

Film (Animated)

In WALL•E, it's implied that the titular robot had at one point or another replaced every part of his body from one of the robot spares he keeps in his house, except his motherboard. So, by the end, when Eve replaces his motherboard after it gets severely damaged, Wall-E acts like any other garbage disposal robot until Eve kisses him.

Film (Live-Action)

The Beast in The World's End. It's had every meaningful part replaced, but looks the same and runs about as junkily as it did in the '90s.

John Dies at the End: The film opens with David beheading a body. However, the handle breaks and he gets the handle replaced. Later on, he chips the head killing a centipede... thing. Eventually, the guy he beheaded comes Back from the Dead, and the reanimated corpse and points to the axe and says "that's the axe that slayed me," to which David asks the audience "is he right?"

Literature

Questioned in The Last King. The narrator wonders if, after replacing each and every part of his grandfather's axe, it is still the same axe.

An early example is the Tin Woodman from The Wonderful Wizard of Oz. He pissed off a witch who enchanted his ax so that it would cut off pieces of him, and he went to a tinsmith to replace the missing parts. Eventually he was made entirely out of tin - but since it was a gradual process, he's still human Nick Chopper and not a new person.

Brought up several times, generally in regards to a Dwarfish axe which has been passed down through the family for generations: sometimes the head needed replacing, other times the shaft, still more times the eye or the bit, but it's still the same ancestral axe.

Played to the hilt in the book's climax, where no one's terribly upset that the conspiracy to influence the Dwarfish succession involved destroying the Scone of Stone and replacing it with a perfect replica: the Scone had already been replaced many times over the centuries, but it had always remained "the thing and the whole of the thing."

Another Discworld novel discusses the example of a witch's broom that is malfunctioning. No matter what part of the broom got replaced - and eventually, all parts of the broom have been replaced at least once - the malfunction stubbornly refused to disappear.

The Belgariad. Alluded to in the Malloreon series. Poledra tells Beldin that she's surprised he hasn't changed his tunic during the thousands of years since she last saw him. Beldin says that he patches it, and replaces the patches as they wear out, to the point that the original tunic "is only a memory".

Honor Harrington mentions that a particular chair has been in the Protector's Palace nursery for over seven hundred years, plus or minus the odd frame repair or reupholstering.

John Dies at the End: Like the film, the book begins with exploring this question. David beheads a body, but the handle breaks on the last swing. He replaces it. He later chips the head on another supernatural creature, and replaces it. When the guy he beheaded comes Back from the Dead, the reanimated corpse points to the axe and says "that's the same axe that beheaded me," to which David asks the reader "is he right?"

In the BattleTech novel Close Quarters this is refered to with an old Jenner 'Mech which is 'one of the first' ever made..except that every single part, down to even the random nuts and bolts, have been replaced over the last 600 years two or three times (or more!).

Happened to Douglas Adams in Last Chance to See when he visits a historical building in China, and finds that it looks suspiciously new. He asks about it and is told that the building burned down, and was rebuilt from all new materials. And that this has happened multiple times. He asks how it's the same building then, and is told "It's always the same building". Adams concludes that someone is missing the point, but that it might be him.

Live Action TV

A popular example comes from the British sit-com Only Fools and Horses, where Trigger, one of the characters, is given a medal for owning the same broom for 20 years, although it has had 17 new heads and 14 new handles. When asked how can it be the same broom, Trigger produces a picture of himself and his broom and asks, "What more proof do you need?"

Discussed in an episode of Star Trek: Deep Space Nine. Kira's Romantic False Lead Bareil Antos gets injured and has part of his brain replaced with cybernetics. As more of his brain fails and is replaced, the less he's him. Eventually he's mostly cybernetics, and rather than continue the process Kira allows him to die.

Discussed and played straight in the Doctor Who episode Deep Breath. The antagonist of the episode is harvesting human organs to be able to pilot the ship, but in doing so, he has replaced most of the ship, and of himself. Capaldi's Doctor lampshades this by saying "If you have a broom, you replace the handle, and then you replace the brush, and do it over and over, is it still the same broom? The answer is no, but you can still sweep the floor, and that's actually irrelevant."

Played for laughs in Cheers when a con artist tries to sell "George Washington's Axe," but then has to explain that all the parts have been replaced over the centuries.

The first warship seen owned by the Tagon's Toughs in Schlock Mercenary was the Dragon-class cruiser Kitsefear. After her destruction early on in the comics, she was eulogized in a footnote that mentioned that "her hull had been patched so many times it's hard to say where the original hull sits."

Web Original

Matt Santoro discusses this paradox in his video The 10 Most MIND-TWISTING Paradoxes of All Time!.

Western Animation

In one episode of Bump in the Night, Molly gradually replaces bits of her body with tougher parts in order to become stronger. As she does so, she gradually becomes more and more cruel and domineering. This culminates in her ripping off her own head, the last part of her original body, and replacing it with a staple remover. Squishington manages to reattach the head to a doll's body, which resets Molly to her original, gentle personality. She then confronts the form she made over the course of the episode, which is still rampaging, and claims to be what Molly always wanted to be. Molly admits she was wrong.

Invoked in the Futurama episode "The Six Million Dollar Mon", in which Hermes continually "upgrades" himself by replacing various organic parts with robotic prostheses. As each human part is removed, Zoidberg salvages it and stitches them back together. After the final organic piece of old!Hermes, the brain, is replaced and reattached to new!Hermes, there are two Hermeses: an organic one with all the parts of the original (plus a whole lot of stitches), and a robotic one controlled by the processor of the psychopathic robot Roberto.

Joked about in an episode of Family Guy. Joan Rivers was doing interviews on the red carpet of the Adult Video Awards, and said that she was once asked to do a porno but couldn't because, since she's had so much plastic surgery, more than 50% of her body was under 18 years of age.

Real Life

A popular but baseless urban legend has it that the human body replaces all of its cells (in some versions, all of its atoms) at regular intervals, usually given as either seven or ten years. While cells do continually die off and are replaced with new ones, they do so at different rates, with no regular cycle of years. There are also exceptions, such as neurons in the brain and parts of the skeletal structure, which last a lifetime and are not replenished.

A number of wooden vessels built during the Age of Sail exist to this day, but over the course of their lifespan they have had numerous refits in which timbers in disrepair or rot were replaced with new material:

The first rate ship-of-the-line HMS Victory, the oldest actively commissioned warship. In a 2009 interview, one of her commanding officers LCDR John Scivier estimated that 10 to 15 percent of her hull remains original.

The frigate USS Constitution, "Old Ironsides," is the oldest active commissioned warship still afloat and sailing. The Naval History and Heritage Command's Boston detachment has also estimated that 10 to 15 percent of her hull is still original.

Unlike Constitution and Victory—which most agree are not replicas—the War of 1812-vintage brig Niagra is more commonly considered a replica rather than the restored original. Her third reconstruction in 1986 found that most of the wood comprising her hull was badly decayed, and so the ship was almost completely rebuilt save for various non-structural timbers which were salvaged and reused.

American philosopher Theodore Sider proposed a solution to this paradox by considering objects from a four-dimensional perspective rather than a three-dimensional one. If objects are thought of as a four-dimensional "river" of three-dimensional "time slices," then each "slice" could still be part of the "river" while remaining unique from one another. In this way, an object can still be considered itself even when all of its components are eventually replaced.

There have been cases of multiple different automobiles each having a claim to being the 'original' vehicle driven by a famous celebrity or racer, as a result of the vehicle having been broken down for parts at some point, leading to there being, for instance, one vehicle based upon the original chassis, another with the original bodywork, and a third with the original engine.

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